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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 66 (1993), S. 493-515 
    ISSN: 0945-3245
    Keywords: 65N55 ; 65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper, we study some additive Schwarz methods (ASM) for thep-version finite element method. We consider linear, scalar, self adjoint, second order elliptic problems and quadrilateral elements in the finite element discretization. We prove a constant bound independent of the degreep and the number of subdomainsN, for the condition number of the ASM iteration operator. This optimal result is obtained first in dimension two. It is then generalized to dimensionn and to a variant of the method on the interface. Numerical experiments confirming these results are reported. As is the case for other additive Schwarz methods, our algorithms are highly parallel and scalable.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 69 (1994), S. 185-211 
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 41A10, 65N30, 65N55
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. In some applications, the accuracy of the numerical solution of an elliptic problem needs to be increased only in certain parts of the domain. In this paper, local refinement is introduced for an overlapping additive Schwarz algorithm for the $p $-version finite element method. Both uniform and variable degree refinements are considered. The resulting algorithm is highly parallel and scalable. In two and three dimensions, we prove an optimal bound for the condition number of the iteration operator under certain hypotheses on the refinement region. This bound is independent of the degree $p $, the number of subdomains $N_r $ and the mesh size $H $. In the general two dimensional case, we prove an almost optimal bound with polylogarithmic growth in $p $.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 68 (1990), S. 6106-6116 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: An exact solution to the problem of collisionless, space-charge-limited flow of cold ions across a one-dimensional (planar) dc plasma sheath of negligible electron density is derived for general values of the presheath ion velocity v0 and electric field E0. For a given ion current density J and sheath thickness d, the exact solution reduces to the classical Child–Langmuir model in the case that v0=0 and E0=0. When either v0 or E0 is sufficiently large, however, the exact solution may differ appreciably from the Child–Langmuir law. The existence of a closed-form expression for the spatial variation of the sheath potential is shown to be contingent upon the satisfaction of a simple inequality relating v0 and E0 to J. When v0 obeys the Bohm criterion and the magnitude of E0 suggests that the Bohm energy is acquired over a distance not less than one Debye length, this inequality is indeed satisfied.
    Type of Medium: Electronic Resource
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  • 4
    Title: Mathematical cardiac electrophysiology /; 13
    Author: Colli Franzone, Piero
    Contributer: Pavarino, Luca F. , Scacchi, Simone
    Publisher: Cham [u.a.] :Springer,
    Year of publication: 2014
    Series Statement: MS&A 13
    ISBN: 978-3-319-04800-0 , 978-3-319-04801-7
    Type of Medium: Book
    Language: English
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